I thought I would do some work on Binary numbers and the UK C(49,6) Lotto, just for fun!
Using the formulas I posted in another thread I setup the Binary number equivialent to the Lexicographic Index Number as a statistical analysis in my DataBase.
I then decided to analyse what the spread of the Binary Digits that were equal to 1 were to see if I could gleam anything interesting from them and maybe use this as a filter.
Well, I found in the UK Lotto that:-
The MINIMUM spread of Binary Digits was 4, with the Binary number 100001010000000000000100 which equates to Lexicographic Index Number 8,716,292 which in turn equates to combination 07 28 34 43 46 48.
The MAXIMUM spread of Binary Digits was 20, with the Binary number 011111111111111111001011 which equates to Lexicographic Index Number 8,388,555 which in turn equates to combination 07 14 20 30 33 46.
I also calculated the spread for ALL C(49,6) combinations and came up with the following table of Binary Digits spread, then the total number of combinations and the percenatge associated with each spread:-
00 = 0 = 0.0000%
01 = 24 = 0.0002%
02 = 276 = 0.0020%
03 = 2,023 = 0.0145%
04 = 10,604 = 0.0758%
05 = 42,274 = 0.3023%
06 = 133,077 = 0.9517%
07 = 338,999 = 2.4242%
08 = 710,455 = 5.0806%
09 = 1,238,718 = 8.8582%
10 = 1,810,028 = 12.9437%
11 = 2,226,188 = 15.9197%
12 = 2,308,910 = 16.5113%
13 = 2,018,590 = 14.4352%
14 = 1,483,701 = 10.6101%
15 = 912,252 = 6.5236%
16 = 465,499 = 3.3288%
17 = 194,853 = 1.3934%
18 = 65,791 = 0.4705%
19 = 17,481 = 0.1250%
20 = 3,520 = 0.0252%
21 = 505 = 0.0036%
22 = 46 = 0.0003%
23 = 2 = 0.0000%
24 = 0 = 0.0000%
Total = 13,983,816 = 100.0000%
As I said, is there any real benefit of knowing this information.
Regards,
PAB
-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-
12:45, restate my assumptions.
(1) Mathematics is the language of nature.
(2) Everything around us can be represented and understood through numbers.
(3) If you graph the numbers of any system, patterns emerge. Therefore, there are patterns, everywhere in nature.
Using the formulas I posted in another thread I setup the Binary number equivialent to the Lexicographic Index Number as a statistical analysis in my DataBase.
I then decided to analyse what the spread of the Binary Digits that were equal to 1 were to see if I could gleam anything interesting from them and maybe use this as a filter.
Well, I found in the UK Lotto that:-
The MINIMUM spread of Binary Digits was 4, with the Binary number 100001010000000000000100 which equates to Lexicographic Index Number 8,716,292 which in turn equates to combination 07 28 34 43 46 48.
The MAXIMUM spread of Binary Digits was 20, with the Binary number 011111111111111111001011 which equates to Lexicographic Index Number 8,388,555 which in turn equates to combination 07 14 20 30 33 46.
I also calculated the spread for ALL C(49,6) combinations and came up with the following table of Binary Digits spread, then the total number of combinations and the percenatge associated with each spread:-
00 = 0 = 0.0000%
01 = 24 = 0.0002%
02 = 276 = 0.0020%
03 = 2,023 = 0.0145%
04 = 10,604 = 0.0758%
05 = 42,274 = 0.3023%
06 = 133,077 = 0.9517%
07 = 338,999 = 2.4242%
08 = 710,455 = 5.0806%
09 = 1,238,718 = 8.8582%
10 = 1,810,028 = 12.9437%
11 = 2,226,188 = 15.9197%
12 = 2,308,910 = 16.5113%
13 = 2,018,590 = 14.4352%
14 = 1,483,701 = 10.6101%
15 = 912,252 = 6.5236%
16 = 465,499 = 3.3288%
17 = 194,853 = 1.3934%
18 = 65,791 = 0.4705%
19 = 17,481 = 0.1250%
20 = 3,520 = 0.0252%
21 = 505 = 0.0036%
22 = 46 = 0.0003%
23 = 2 = 0.0000%
24 = 0 = 0.0000%
Total = 13,983,816 = 100.0000%
As I said, is there any real benefit of knowing this information.
Regards,
PAB
-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-
12:45, restate my assumptions.
(1) Mathematics is the language of nature.
(2) Everything around us can be represented and understood through numbers.
(3) If you graph the numbers of any system, patterns emerge. Therefore, there are patterns, everywhere in nature.
.